Non-iterative One-step Solution for Point Set Registration Problem on Pose Estimation without Correspondence

In this work, we propose to directly find the one-step solution for the point set registration problem without correspondences. Inspired by the Kernel Correlation method, we consider the fully connected objective function between two point sets, thus avoiding the computation of correspondences. By utilizing least square minimization, the transformed objective function is directly solved with existing well-known closed-form solutions, e.g., singular value decomposition, that is usually used for given correspondences. However, using equal weights of costs for each connection will degenerate the solution due to the large influence of distant pairs. Thus, we additionally set a scale on each term to avoid high costs on non-important pairs. As in feature-based registration methods, the similarity between descriptors of points determines the scaling weight. Given the weights, we get a one step solution. As the runtime is in $\mathcal O (n^2)$, we also propose a variant with keypoints that strongly reduces the cost. The experiments show that the proposed method gives a one-step solution without an initial guess. Our method exhibits competitive outlier robustness and accuracy, compared to various other methods, and it is more stable in case of large rotations. Additionally, our one-step solution achieves a performance on-par with the state-of-the-art feature based method TEASER

Dependent landmark drift: robust point set registration with a Gaussian mixture model and a statistical shape model

The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area can often elegantly solve the problems without using geometric information specific to the objects. This means that registration performance can be further improved by using prior knowledge of object geometry. In this paper, we propose a novel point set registration method using the Gaussian mixture model with prior shape information encoded as a statistical shape model. Our transformation model is defined as a combination of the similar transformation, motion coherence, and the statistical shape model. Therefore, the proposed method works effectively if the target point set includes outliers and missing regions, or if it is rotated. The computational cost can be reduced to linear, and therefore the method is scalable to large point sets. The effectiveness of the method will be verified through comparisons with existing algorithms using datasets concerning human body shapes, hands, and faces

Non-iterative rigid 2D/3D point-set registration using semidefinite programming

We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINP) formulations of the 2D/3D registration problem when there are multiple 2D images, and propose convex relaxations for both of the MINPs to semidefinite programs (SDP) that can be solved efficiently by interior point methods. Our approach to the 2D/3D registration problem is non-iterative in nature as we jointly solve for pose and correspondence. Furthermore, these convex programs can readily incorporate feature descriptors of points to enhance registration results. We prove that the convex programs exactly recover the solution to the original nonconvex 2D/3D registration problem under noiseless condition. We apply these formulations to the registration of 3D models of coronary vessels to their 2D projections obtained from multiple intra-operative fluoroscopic images. For this application, we experimentally corroborate the exact recovery property in the absence of noise and further demonstrate robustness of the convex programs in the presence of noise.Comment: 15 pages, 7 figure

Model-Driven Feed-Forward Prediction for Manipulation of Deformable Objects

Robotic manipulation of deformable objects is a difficult problem especially because of the complexity of the many different ways an object can deform. Searching such a high dimensional state space makes it difficult to recognize, track, and manipulate deformable objects. In this paper, we introduce a predictive, model-driven approach to address this challenge, using a pre-computed, simulated database of deformable object models. Mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity, and stored in a database for fast and efficient retrieval. To validate this approach, we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task. First, the database is used for category and pose estimation for a garment in an arbitrary position. A fully featured 3D model of the garment is constructed in real-time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose. Second, the database can significantly benefit the manipulation of deformable objects via non-rigid registration, providing accurate correspondences between the reconstructed object model and the database models. Third, the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects, such as the folding of garments. Extensive experimental results are shown for the tasks above using a variety of different clothing.Comment: 21 pages, 27 figure

3D Scan Registration using Curvelet Features in Planetary Environments

Topographic mapping in planetary environments relies on accurate 3D scan registration methods. However, most global registration algorithms relying on features such as FPFH and Harris-3D show poor alignment accuracy in these settings due to the poor structure of the Mars-like terrain and variable resolution, occluded, sparse range data that is hard to register without some a-priori knowledge of the environment. In this paper, we propose an alternative approach to 3D scan registration using the curvelet transform that performs multi-resolution geometric analysis to obtain a set of coefficients indexed by scale (coarsest to finest), angle and spatial position. Features are detected in the curvelet domain to take advantage of the directional selectivity of the transform. A descriptor is computed for each feature by calculating the 3D spatial histogram of the image gradients, and nearest neighbor based matching is used to calculate the feature correspondences. Correspondence rejection using Random Sample Consensus identifies inliers, and a locally optimal Singular Value Decomposition-based estimation of the rigid-body transformation aligns the laser scans given the re-projected correspondences in the metric space. Experimental results on a publicly available data-set of planetary analogue indoor facility, as well as simulated and real-world scans from Neptec Design Group's IVIGMS 3D laser rangefinder at the outdoor CSA Mars yard demonstrates improved performance over existing methods in the challenging sparse Mars-like terrain.Comment: 27 pages in Journal of Field Robotics, 201

Fast and Accurate Point Cloud Registration using Trees of Gaussian Mixtures

Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, SLAM, object/scene recognition, and augmented reality. In this paper, we present a new registration algorithm that is able to achieve state-of-the-art speed and accuracy through its use of a hierarchical Gaussian Mixture Model (GMM) representation. Our method constructs a top-down multi-scale representation of point cloud data by recursively running many small-scale data likelihood segmentations in parallel on a GPU. We leverage the resulting representation using a novel PCA-based optimization criterion that adaptively finds the best scale to perform data association between spatial subsets of point cloud data. Compared to previous Iterative Closest Point and GMM-based techniques, our tree-based point association algorithm performs data association in logarithmic-time while dynamically adjusting the level of detail to best match the complexity and spatial distribution characteristics of local scene geometry. In addition, unlike other GMM methods that restrict covariances to be isotropic, our new PCA-based optimization criterion well-approximates the true MLE solution even when fully anisotropic Gaussian covariances are used. Efficient data association, multi-scale adaptability, and a robust MLE approximation produce an algorithm that is up to an order of magnitude both faster and more accurate than current state-of-the-art on a wide variety of 3D datasets captured from LiDAR to structured light.Comment: ECCV 201

Unrestricted Facial Geometry Reconstruction Using Image-to-Image Translation

It has been recently shown that neural networks can recover the geometric structure of a face from a single given image. A common denominator of most existing face geometry reconstruction methods is the restriction of the solution space to some low-dimensional subspace. While such a model significantly simplifies the reconstruction problem, it is inherently limited in its expressiveness. As an alternative, we propose an Image-to-Image translation network that jointly maps the input image to a depth image and a facial correspondence map. This explicit pixel-based mapping can then be utilized to provide high quality reconstructions of diverse faces under extreme expressions, using a purely geometric refinement process. In the spirit of recent approaches, the network is trained only with synthetic data, and is then evaluated on in-the-wild facial images. Both qualitative and quantitative analyses demonstrate the accuracy and the robustness of our approach.Comment: To appear in ICCV 201

Point-Set Registration: Coherent Point Drift

Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown non-rigid spatial transformation, large dimensionality of point set, noise and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and non-rigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the GMM centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by re-parametrization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the non-rigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and non-rigid transformations in the presence of noise, outliers and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial perception is jeopardized by the presence of incorrect data association, and in general, outliers. Although techniques to handle outliers do exist, they can fail in unpredictable manners (e.g., RANSAC, robust estimators), or can have exponential runtime (e.g., branch-and-bound). In this paper, we advance the state of the art in outlier rejection by making three contributions. First, we show that even a simple linear instance of outlier rejection is inapproximable: in the worst-case one cannot design a quasi-polynomial time algorithm that computes an approximate solution efficiently. Our second contribution is to provide the first per-instance sub-optimality bounds to assess the approximation quality of a given outlier rejection outcome. Our third contribution is to propose a simple general-purpose algorithm, named adaptive trimming, to remove outliers. Our algorithm leverages recently-proposed global solvers that are able to solve outlier-free problems, and iteratively removes measurements with large errors. We demonstrate the proposed algorithm on three spatial perception problems: 3D registration, two-view geometry, and SLAM. The results show that our algorithm outperforms several state-of-the-art methods across applications while being a general-purpose method

Robust Registration and Geometry Estimation from Unstructured Facial Scans

Commercial off the shelf (COTS) 3D scanners are capable of generating point clouds covering visible portions of a face with sub-millimeter accuracy at close range, but lack the coverage and specialized anatomic registration provided by more expensive 3D facial scanners. We demonstrate an effective pipeline for joint alignment of multiple unstructured 3D point clouds and registration to a parameterized 3D model which represents shape variation of the human head. Most algorithms separate the problems of pose estimation and mesh warping, however we propose a new iterative method where these steps are interwoven. Error decreases with each iteration, showing the proposed approach is effective in improving geometry and alignment. The approach described is used to align the NDOff-2007 dataset, which contains 7,358 individual scans at various poses of 396 subjects. The dataset has a number of full profile scans which are correctly aligned and contribute directly to the associated mesh geometry. The dataset in its raw form contains a significant number of mislabeled scans, which are identified and corrected based on alignment error using the proposed algorithm. The average point to surface distance between the aligned scans and the produced geometries is one half millimeter